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Temperature-reducing shocks in optically-thin radiative MHD -- analytical and numerical results

Ben Snow

Abstract

Shocks are often invoked as heating mechanisms in astrophysical systems, with both adiabatic compression and dissipative heating that leading to temperature increases. Whilst shocks are reasonably well understood for ideal magnetohydrodynamic (MHD) systems, in many astrophysical plasmas, radiation is an important phenomena, which can allow energy to leave the system. As such, energy becomes non-conservative which can fundamentally change the behaviour of shocks. The energy emitted through optically-thin radiation post-shock can exceed the thermal energy increase, resulting in shocks that reduce the temperature of the medium, i.e., cooling shocks that have a net decrease in temperature across the interface. In this paper, semi-analytical solutions for radiative shocks are derived to demonstrate that both cooling (temperature decreasing) and heating (temperature increasing) shock solutions are possible in radiative MHD. Numerical simulations of magnetic reconnection with optically-thin radiative losses also yield both heating and cooling shocks in roughly equal abundances. The detected cooling shocks feature a significantly lower pressure jump across the shock than their heating counterparts. The compression at the shock front leads to locally-enhanced radiative losses, resulting in significant cooling within a few grid cells in the upstream and downstream directions. The presence of temperature-reducing (cooling) shocks is critical in determining the thermal evolution, and heating or cooling, across a wealth of radiative astrophysical plasmas.

Temperature-reducing shocks in optically-thin radiative MHD -- analytical and numerical results

Abstract

Shocks are often invoked as heating mechanisms in astrophysical systems, with both adiabatic compression and dissipative heating that leading to temperature increases. Whilst shocks are reasonably well understood for ideal magnetohydrodynamic (MHD) systems, in many astrophysical plasmas, radiation is an important phenomena, which can allow energy to leave the system. As such, energy becomes non-conservative which can fundamentally change the behaviour of shocks. The energy emitted through optically-thin radiation post-shock can exceed the thermal energy increase, resulting in shocks that reduce the temperature of the medium, i.e., cooling shocks that have a net decrease in temperature across the interface. In this paper, semi-analytical solutions for radiative shocks are derived to demonstrate that both cooling (temperature decreasing) and heating (temperature increasing) shock solutions are possible in radiative MHD. Numerical simulations of magnetic reconnection with optically-thin radiative losses also yield both heating and cooling shocks in roughly equal abundances. The detected cooling shocks feature a significantly lower pressure jump across the shock than their heating counterparts. The compression at the shock front leads to locally-enhanced radiative losses, resulting in significant cooling within a few grid cells in the upstream and downstream directions. The presence of temperature-reducing (cooling) shocks is critical in determining the thermal evolution, and heating or cooling, across a wealth of radiative astrophysical plasmas.
Paper Structure (15 sections, 17 equations, 7 figures)

This paper contains 15 sections, 17 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Rankine-Hugoniot jump conditions (no losses)
  4. Radiative shock jumps
  5. Semi-analytic shock solution
  6. Hazy Cooling Curve
  7. Limitations of the analytical solutions
  8. Numerical Simulation of Tearing Instability
  9. Shock Detection
  10. Discussion
  11. Model assumptions
  12. Interstellar medium
  13. Relation to the thermal stability
  14. Conclusion
  15. Shock solutions for different plasma$-\beta$ and $\theta$

Figures (7)

  • Figure 1: Panel (a) (blue line) Normalised radiative loss curve using CHIANTI v9 Dere1997Dere2019 with the default abundance file. The blue and green vertical lines show the upstream and possible downstream temperatures for a shock with $r=2$, as discussed towards the end of \ref{['Sec:RadShock']}. The orange line is the modified version of the loss curve used in the simulation of Section \ref{['Sec:Simulation']}. Panels (b)-(e) Example radiative MHD solutions for reference upstream values of $\beta=0.1,\theta=\pi/8,T^u=10^5$K compared to the MHD solution (black line). The radiative MHD shock solutions are coloured by the temperature jump, with red denoting heating solution, blue denoting cooling solutions, and effectively isothermal solutions in green. Reference upstream temperatures are $T^u=1.8\times 10^4 (b),5.0\times 10^4 (c),2.3\times 10^5 (d),5\times 10^5 (e), 10^6 (f)$
  • Figure 2: (a) Hazy cooling curve normalised to unity at the peak. The radiative shock solutions are for usptream temperatures of $10^3$K (b), $10^4$K (c), $10^5$K (d), $10^6$K (e), and $10^7$K. The upstream temperatures correspond to the vertical lines in panel (a).
  • Figure 3: Numerical simulation of the tearing instability at time $t=40$ coloured by the temperature, with the identified slow-mode shocks highlighted in red.
  • Figure 4: Histogram of the temperature jump of the detected slow-mode shocks in the tearing instability coloured.
  • Figure 5: Scatter plot of the compression vs the temperature jump for the detected slow-mode shocks, coloured by the pressure jump
  • ...and 2 more figures